How can I merge vertices into an object in Blender?
It looks like you projected the contour of the same object onto it's side, thus i believe the newly generated vertices should be lying on the edges of the object you want to connect them to. 
Since you want to merge them, i can offer 2 ways:


Join the mesh objects and then cut the faces that you want the vertices to be merged into with the knife tool. The new generated cut gives you new vertices that should all be lying on the same edge as the vertices you want to merge, thus selecting each vertex per edge from the new cut and merging it to the vertex from the projection would result in a merged geometry with the projected vertices incorporated.
Merging the 2 mesh objects (object and the projected vertices object), then delete the faces&amp;edges that cross the projected vertices. Afterwards just bridge the edges left and right from the vertices projected to the edge of the projected vertices. Closing the gap again and essentially merging all into one editable mesh as well.


You could depending on what is easier use both options. But since you used the contour of the object to project onto its side, i believe the second solution might be easier.